Market Power

• When an individual agent can affect the price (or other outcome) that prevails in the market, the agent has market power

• A monopoly market consists of a single seller facing many buyers

• A monopsony market consists of a single buyer facing many sellers

Monopoly

• In contrast to a perfectly competitive firm, a monopolist sets the market price of its product (market power)

• The demand curve stops the monopolist from setting an infinitely high price by imposing a trade-off

  • The higher the price, the lower the quantity it sells
  • The lower the price, the higher the quantity it sells

Monopolist’s Demand Curve

Monopolist’s Problem

The monopolist’s profit-maximization problem : \[ \begin{aligned} \max_Q \pi(Q)&=TR(Q)-TC(Q) \\ \text{s.t. }& TR(Q)=QP(Q) \end{aligned} \qquad(1)\]

• where \(P(Q)\) is the inverse market demand

Optimality Condition

1. Profits are maximized at \(Q^*\) such that \(MR(Q^*)=MC(Q^*)\)

2. Slope of the \(MC\) curve exceeds the slope of the \(MR\) curve

Optimality Condition

Elasticity

Marginal Revenue

Marginal Revenue

Competitive firms is not affected by the change in price due to its change in output

Marginal Revenue

• Marginal revenue has two parts:

  • \(P\): increase in revenue due to higher volume -the marginal units
  • \(Q(dP(Q)/dQ)\): decrease in revenue due to reduced price of the inframarginal units (negative)

• The marginal revenue is less than the price the monopolist can charge to sell that quantity for any \(Q\ge0\) because \(dP(Q)/dQ\le0\)

• MR can be positive or negative

Profit-Maximization Condition

Suppose the monopolist faces a linear demand curve

\[ P(Q)=a-bQ \]

Then, the revenue function is

\[ TR(Q)=QP(Q)=aQ-bQ^2 \]

and the marginal revenue function is

\[ MR(Q)=a-2bQ \]

Profit-Maximization Condition

Monopoly vs Competitive Market

• \(P_M>MC_M\), in general \(P_M > P_{PC}\)
• \(Q^*_{M} < Q^*_{PC}\)
• \(\pi_{M}\ge0\)
• Consumers are worse off but the firm is better off. What’s best?

Monopoly is not Pareto Efficient

• Pareto Efficiency: There is no way to make someone better off without making somebody else worse off

• Inverse demand curve: At each level of output, \(P(Q)\) measures how much people are willing to pay for an additional unit of the good

Monopoly is not Pareto Efficient

• Since \(P(Q)\ge MC(Q)\) for all output levels between \(Q_M\) and \(Q_C\)

• There is a range of consumers that are willing to pay \(\bar P\) for an extra unit of output, such that \(P(Q)>\bar P> MC(Q)\) (area under demand curve between \(Q_M\) and \(Q_C\) and above the \(MC(Q)\))

Inefficiency of Monopoly

• Any of these consumers would be better off because they are willing to pay \(P(Q)\) but the extra unit of output is sold at \(\bar P < P(Q)\)

• Likewise, the firm would be better off because it cost \(MC(Q)\) to produce the extra unit of output and the firms sold it for \(\bar P > MC(Q)\)(all the other units of output are being sold for the same price \(P_M\) as before)

• We found a Pareto improvement!

Inefficiency of Monopoly (continued)

Welfare Economics of Monopoly

• How inefficient is a Monopoly?

• Compare changes in producer’s and consumer’s surplus from a movement from Monopoly to Perfect Competition

• Change in producer’s surplus —firm’s profits— measures how much the owners would be willing to pay to get the higher price under monopoly

• Change in consumers’ surplus measures how much the consumers would have to be paid to compensate them for the higher price

Deadweight Loss of Monopoly

Deadweight Loss of Monopoly

No Unique Supply Curve for Monopolists

• In Competitive Markets, \(P=MC(Q)\), there is a unique relationship between the quantity produced by the firm and price \(Q=MC^{-1}(P)\)

• In Monopoly, \(P+Q\frac{dP(Q)}{dQ}=MC(Q)\)

• Depending on the shape of the demand curve,\(\frac{dP(Q)}{dQ}\), the monopolist might produce the same quantity at two different prices or produce different quantities at the same price

  • no unique relationship between \(Q\) and \(P\), \(\implies\) no unique supply curve

No Unique Supply Curve

Elasticity of Demand

\[ \begin{aligned} MR(Q)&=P+Q\frac{dP(Q)}{dQ} \\ &=P\left(1+\frac{Q}{P}\frac{dP(Q)}{dQ} \right)\\ &=P\left(1+\frac{1}{\frac{P}{Q}\frac{dQ}{dP}}\right)\\ &=P\left(1+\frac{1}{\epsilon_{Q,P}}\right) \\ &=P\left(1-\frac{1}{|\epsilon_{Q,P}|}\right) \end{aligned} \]

Last line follows because price elasticity of demand \(\epsilon_{Q,P}<0\)

Elasticity of Demand

Optimality Condition Graph

Elastic Part of the Curve

• Monopolists will never choose to operate where the demand is inelastic

1. \(MC\ge0\), at the optimum \(MR=MC\ge0\), but \(|\epsilon_{Q,P}|<1 \implies MR <0\)

2. Any point were \(|\epsilon_{Q,P}|<1\) cannot be a profit maximum, since the monopolist could increase profits by producing less output

Pricing Rule

Profit maximizing condition is \(MR = MC\) with \(P^*\) and \(Q^*\)

\[ \begin{aligned} 𝑀𝑅(𝑄^∗ )&=𝑀𝐶(𝑄^∗ ) \\ 𝑃^∗ \left(1-\frac{1}{|\epsilon_{𝑄,𝑃}|}\right)&=𝑀𝐶(𝑄^∗) \end{aligned} \]

Rearranging and setting MR(Q) = MC(Q) \[ \frac{(𝑃^∗−𝑀C^∗)}{𝑃^∗} =\frac{1}{ |\epsilon_{𝑄,𝑃}| } \]

Inverse elasticity pricing rule (IEPR): The less price elastic the demand, the higher the optimal markup

Market Power

• When a firm can exercise some degree of control over its price in the market, we say that it has market power

• Monopolists or producers of differentiated products will, in general, charge prices that exceed their marginal cost

• A natural measure of market power is \((P − MC)/P\)

  • Lerner Index

• The Lerner Index is zero for a perfectly competitive industry. It is positive for any industry that departs from perfect competition.

Market Power

• The IEPR tells us that in the equilibrium of a monopoly market, the Lerner Index will be inversely related to the market price elasticity of demand.

• An important driver of the price elasticity of demand is the threat of substitute products outside the industry

• If a monopoly market faces strong competition from substitute products, the Lerner Index can still be low. In other words, a firm might have a monopoly, but its market power might still be weak.

Why Monopolies Exist?

• Read Ch. 11.6

• Natural Monopolies

  • Economies of scale
  • Demand

• Barriers to entry

  • Structural
  • Legal
  • Strategic

Monopsony

• A monopsony market consists of a single buyer facing many sellers

• The monopsonist’s profit maximization problem:

  • \(\max \pi = TR – TC = Pf(L) – w(L)L\)
  • where: \(Pf(L)\) is the total revenue for the monopsonist
  • and \(w(L)L\) is the total cost

• The monopsonist’s profit maximization condition:

  • \(MRP_L = ME_L\)
  • \(P \times MP_L = dTC/dL\)
  • \(P (dQ/dL) = w + L (dw/dL)\)

Inverse Elasticity Pricing Rule

• Monopsony equilibrium condition results in:
  • \((MRP_L−w)/w=1/\epsilon_{L,w}\)
  • where: \(\epsilon_{L,w}\) is the price elasticity of labor supply, \((w/L)(dL/dw)\)